Systolic inequalities for Reeb flows in dimension 3

• Grant number: 17/26620-6
• Support Opportunities: Scholarships abroad - Research
• Start date: March 01, 2018
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Pedro Antonio Santoro Salomão
• Grantee: Pedro Antonio Santoro Salomão
• Host Investigator: Alberto Abbondandolo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: Ruhr-Universität Bochum (RUB), Germany
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

The study of systolic inequalities for Reeb flows in dimension 3 has been very active recently. The ratio of the square of the least action of a closed Reeb orbit and the contact volume is called the systolic ratio. It is a difficult question to determine upper bounds of the systolic ratio for certain classes of Reeb flows. In general, no such upper bound exists. In this project we intend to continue the research on systolic inequalities in collaboration with A. Abbondandolo e B Bramham (both from Ruhr Universitat) e U. Hryniewicz (UFRJ). (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ABBONDANDOLO, ALBERTO; BRAMHAM, BARNEY; HRYNIEWICZ, UMBERTO L.; SALOMAO, PEDRO A. S.. SHARP SYSTOLIC INEQUALITIES FOR RIEMANNIAN AND FINSLER SPHERES OF REVOLUTION. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 374, n. 3, p. 1815-1845, MAR 2021. (17/26620-6)